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  • Cited by 1369
Publisher:
Cambridge University Press
Online publication date:
November 2012
Print publication year:
2012
Online ISBN:
9781139043816

Book description

Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.

Reviews

'This book is a welcome addition to the rapidly developing area of applications of stochastic geometric models to telecommunications.'

Ilya S. Molchanov - American Mathematical Society

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Contents

References
References
Alon, N. & Spencer, J. (2008), The Probabilistic Method, 3rd edn., Wiley.
Andrews, J. G., Baccelli, F. & Ganti, R. K. (2011), A tractable approach to coverage and rate in cellular networks, IEEE Transactions on Communications 59(11), 3122–3134.
Athreya, K. B. & Ney, P. E. (2004), Branching Processes, Dover Publications.
Baccelli, F. & Blaszczyszyn, B. (2009), Stochastic Geometry and Wireless Networks, NOW.
Baccelli, F., Blaszczyszyn, B. & Mirsadeghi, M. O. H. (2011), Optimal paths on the space–time SINR random graph, Advances in Applied Probability 43(1), 131–150.
Baccelli, F., Blaszczyszyn, B. & Mühlethaler, P. (2006), An ALOHA protocol for multihop mobile wireless networks, IEEE Transactions on Information Theory 52(2), 421–436.
Baddeley, A. J. & Silverman, B. W. (1984), A cautionary example on the use of second-order methods for analyzing point patterns, Biometrics 40(4), 1089–1093.
Baddeley, A. & Turner, R. (2005), Spatstat: an R package for analyzing spatial point patterns, Journal of Statistical Software 12(6), 1–42.
Baddeley, A. J. & van Lieshout, M. N. M. (1995), Area-interaction point processes, Annals of the Institute of Statistical Mathematics 47(4), 601–619.
Baddeley, A., Bárány, I., Schneider, R. & Weil, W. (2007), Stochastic Geometry, Springer.
Balister, P., Bollobás, B., Sarkar, A. & Walters, M. (2005), Connectivity of random k-nearest-neighbor graphs, Advances in Applied Probability 37, 1–24.
Balister, P., Bollobás, B., Sarkar, A. & Walters, M. (2010), Sentry selection in wireless networks, Advances in Applied Probability 42(1), 1–25.
Balister, P., Bollobás, B. & Walters, M. (2004), Continuum percolation with steps in an annulus, Annals of Applied Probability 14, 1869–1879.
Balister, P., Bollobás, B. & Walters, M. (2005), Continuum percolation with steps in the square or the disc, Random Structures and Algorithms 26(4), 392–403.
Barbour, A. D. & Chen, L. H. Y. (2005), Stein's Method and Applications, SingaporeUniversity Press.
Bedford, T. & van den Berg, J. (1997), A remark on the Van Lieshout and Baddeley J function for point processes, Advances in Applied Probability 29(1), 19–25.
Bollobás, B. (2001), Random Graphs, 2nd edn., Cambridge University Press.
Bollobás, B. & Riordan, O. (2006), Percolation, Cambridge University Press.
Broadbent, S. & Hammersley, J. (1957), Percolation processes I. Crystals and mazes, Proceedings of the Cambridge Philosophical Society 53, 629–641.
Campbell, N. (1909), The study of discontinuous phenomena, Mathematical Proceedings of the Cambridge Philosophical Society 15, 117–136.
Cressie, N. (1993), Statistics for Spatial Data, revised edn., Wiley.
Daley, D. J. & Vere-Jones, D. (2003), An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods, 2nd edn., Springer.
Daley, D. J. & Vere-Jones, D. (2008), An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure, 2nd edn., Springer.
Dhillon, H. S., Ganti, R. K., Baccelli, F. & Andrews, J. G. (2012), Modeling and analysis of K-tier downlink heterogeneous cellular networks, IEEE Journal on Selected Areas in Communications 30(3), 550–560.
Dousse, O., Franceschetti, M., Macris, N., Meester, R. & Thiran, P. (2006), Percolation in the signal-to-interference ratio graph, Journal of Applied Probability 43(2), 552–562.
Durrett, R. (1985), Some general results concerning the critical exponents of percolation, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 69, 421–437.
Fekete, M. (1923), Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahigen Koeffizienten, Mathematische Zeitschrift 17(1), 228–249.
Fortuin, C. M., Kasteleyn, P. W. & Ginibre, J. (1971), Correlation inequalities on some partially ordered sets, Communications in Mathematical Physics 22(2), 89–103.
Franceschetti, M. & Meester, R. (2007), Random Networks for Communication: From Statistical Physics to Information Systems, Cambridge University Press.
Franceschetti, M., Booth, L., Cook, M., Bruck, J. & Meester, R. (2005), Continuum percolation with unreliable and spread out connections, Journal of Statistical Physics 118(3/4), 721–734.
Ganti, R. K. & Haenggi, M. (2007), Dynamic connectivity and packet propagation delay in ALOHA wireless networks, in 41st Asilomar Conference on Signals, Systems, and Computers (Asilomar '07), Pacific Grove, CA.
Ganti, R. K. & Haenggi, M. (2009a), Interference and outage in clustered wireless ad hoc networks, IEEE Transactions on Information Theory 55(9), 4067–4086.
Ganti, R. K. & Haenggi, M. (2009b), Spatial and temporal correlation of the interference in ALOHA ad hoc networks, IEEE Communications Letters 13(9), 631–633.
Ganti, R. K. & Haenggi, M. (2012), Dynamic connectivity and path formation time in Poisson networks, The Journal of Mobile Communication, Computation and Information, http://www.nd.edu/~mhaenggi/pubs/winet12.pdf.
Ganti, R. K., Andrews, J. G. & Haenggi, M. (2011), High-SIR transmission capacity of wireless networks with general fading and node distribution, IEEE Transactions on Information Theory 57(5), 3100–3116.
Georgii, H.-O. (1976), Canonical and grand canonical Gibbs states for continuum systems, Communications in Mathematical Physics 48(1), 31–51.
Giacomelli, R., Ganti, R. K. & Haenggi, M. (2011), Outage probability of general ad hoc networks in the high-reliability regime, IEEE/ACM Transactions on Networking 19(4), 1151–1163.
Grandell, J. (1976), Doubly Stochastic Poisson Processes, Springer.
Grimmett, G. (1999), Percolation, 2nd edn., Springer.
Haenggi, M. (2008a), A geometric interpretation of fading in wireless networks: theory and applications, IEEE Transactions on Information Theory 54(12), 5500–5510.
Haenggi, M. (2008b), The secrecy graph and some of its properties, in 2008 IEEE International Symposium on Information Theory (ISIT '08), Toronto.
Haenggi, M. (2009), Outage, local throughput, and capacity of random wireless networks, IEEE Transactions on Wireless Communications 8(8), 4350–4359.
Haenggi, M. (2011), Mean interference in hard-core wireless networks, IEEE Communications Letters 15(8), 792–794.
Haenggi, M. & Ganti, R. K. (2008), Interference in Large Wireless Networks, NOW.
Hall, P. (1985), On the coverage of k-dimensional space by k-dimensional spheres, The Annals of Probability 13(3), 991–1002.
Harris, T. E. (1960), A lower bound on the critical probability in a certain percolation process, Mathematical Proceedings of the Cambridge Philosophical Society 56, 13–20.
Heinrich, L. & Schmidt, V. (1985), Normal convergence of multidimensional shot noise and rates of this convergence, Advances in Applied Probability 17(4), 709–730.
Illian, J., Penttinen, A., Stoyan, H. & Stoyan, D. (2008), Statistical Analysis and Modeling of Spatial Point Patterns, Wiley.
Ilow, J. & Hatzinakos, D. (1998), Analytical alpha-stable noise modeling in a Poisson field of interferers or scatterers, IEEE Transactions on Signal Processing 46(6), 1601–1611.
Isham, V. (1984), Multitype Markov point processes: some approximations, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 391, 39–53.
Jacobsen, M. (2006), Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes, Birkhäuser.
Janson, S., Luczak, T. & Rucinski, A. (2000), Random Graphs, Wiley-Interscience.
Kesten, H. (1980), The critical probability of bond percolation on the square lattice equals 1/2, Communications in Mathematical Physics 74(1), 41–59.
Kingman, J. F. C. (1978), Uses of exchangeability, The Annals of Probability 6(2), 183–197.
Kingman, J. F. C. (1993), Poisson Processes, Oxford Science Publications.
Lee, C.-H. & Haenggi, M. (2012), Interference and outage in Poisson cognitive networks, IEEE Transactions on Wireless Communications 11(4), 1392–1401.
Lindvall, T. (2002), Lectures on the Coupling Method, Dover Publications.
Linnartz, J.-P. M. G. (1992), Exact analysis of the outage probability in multiple-user radio, IEEE Transactions on Communications 40(1), 20–23.
Lowen, S. B. & Teich, M. C. (1990), Power-law shot noise, IEEE Transactions on Information Theory 36(6), 1302–1318.
Matérn, B. (1986), Spatial Variation, 2nd edn., Springer.
Mathai, A. M. (1999), An Introduction to Geometrical Probability, Gordon and Breach Science Publishers.
Mathar, R. & Mattfeldt, J. (1995), On the distribution of cumulated interference power in Rayleigh fading channels, Wireless Networks 1(1), 31–36.
Matthes, K., Kerstan, J. & Mecke, J. (1978), Infinitely Divisible Point Processes, John Wiley & Sons.
Meester, R. & Roy, R. (1996), Continuum Percolation, Cambridge University Press.
Musa, S. & Wasylkiwskyj, W. (1978), Co-channel interference of spread spectrum systems in a multiple user environment, IEEE Transactions on Communications 26(10), 1405–1413.
Newman, D. S. (1970), A new family of point processes which are characterized by their second moment properties, Journal of Applied Probability 7(2), 338–358.
Newman, M. E. J. & Ziff, R. M. (2000), Fast Monte Carlo algorithm for site or bond percolation, Physical Review Letters 85(19), 4104–4107.
Neyman, J. & Scott, E. L. (1952), A theory of the spatial distribution of galaxies, Astrophysical Journal 116, 144–163.
Neyman, J. & Scott, E. L. (1958), Statistical approach to problems of cosmology, Journal of the Royal Statistical Society, SeriesB 20(1), 1–43.
Nguyen, X. X. & Zessin, H. (1979), Integral and differential characterization of the Gibbs process, Mathematische Nachrichten 88, 105–115.
Peierls, R. (1936), On Ising's model of ferromagnetism, Mathematical Proceedings of the Cambridge Philosophical Society 32, 477–481.
Penrose, M. (2003), Random Geometric Graphs, Oxford University Press.
Rényi, A. (1967), Remarks on the Poisson process, Studia Scientifica Mathematica Hungarica 2, 119–123.
Rice, S. O. (1944), Mathematical analysis of random noise, Bell System Technical Journal 23, 282–332.
Ripley, B. D. (1976), The second-order analysis of stationary point processes, Journal of Applied Probability 13, 255–266.
Samorodnitsky, G. & Taqqu, M. S. (1994), Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall.
Sarkar, A. & Haenggi, M. (2011), Percolation in the secrecy graph. ArXiv, http://arxiv.org/abs/1107.4613.
Sarkar, A. & Haenggi, M. (2012), Secrecy coverage, Internet Mathematics. Available at http://www.nd.edu/~mhaenggi/pubs/im12.pdf.
Schottky, W. (1918), Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern, Annalen der Physik 57, 541–567.
Sousa, E. S. (1990), Interference modeling in a direct-sequence spread-spectrum packet radio network, IEEE Transactions on Communications 38(9), 1475–1482.
Sousa, E. S. & Silvester, J. A. (1990), Optimum transmission ranges in a direct-sequence spread-spectrum multihop packet radio network, IEEE Journal on Selected Areas in Communications 8(5), 762–771.
Spencer, J. (2001), The Strange Logic of Random Graphs, Springer.
Srinivasa, S. & Haenggi, M. (2010), Distance distributions in finite uniformly random networks: theory and applications, IEEE Transactions on Vehicular Technology 59(2), 940–949.
Stoyan, D., Kendall, W. S. & Mecke, J. (1995), Stochastic Geometry and its Applications, 2nd edn., John Wiley & Sons.
Takagi, H. & Kleinrock, L. (1984), Optimal transmission ranges for randomly distributed packet radio terminals, IEEE Transactions on Communications 32(3), 246–257.
van Lieshout, M. N. M. (2000), Markov Point Processes and their Applications, Imperial College Press.
van Lieshout, M. N. M. (2011), A J-function for inhomogeneous point processes, Statistica Neerlandica 65(2), 183–201.
van Lieshout, M. N. M. & Baddeley, A. J. (1996), A nonparametric measure of spatial interaction in point patterns, Statistica Neerlandica 50(3), 344–361.
Walters, M. (2012), Small components in k-nearest neighbour graphs, Discrete Applied Mathematics.
Weber, S. & Andrews, J. G. (2012), Transmission Capacity of Wireless Networks, NOW.
Weber, S., Yang, X., Andrews, J. G. & de Veciana, G. (2005), Transmission capacity of wireless ad hoc networks with outage constraints, IEEE Transactions on Information Theory 51(12), 4091–4102.
Westcott, M. (1972), The probability generating functional, Journal of the Australian Mathematical Society 14, 448–466.
Zorzi, M. & Pupolin, S. (1995), Optimum transmission ranges in multihop packet radio networks in the presence of fading, IEEE Transactions on Communications 43(7), 2201–2205.

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